Followers of Congress should build some flexibility into their Columbus Day travel plans.

Leadership on both sides of the Capitol said it was too early to discuss changes to the schedule, but there’s no way lawmakers would be out of town for a government default. The House and Senate are scheduled to take a regular October break the week of the Columbus Day holiday, which falls on Oct. 14.

Treasury Secretary Jacob J. Lew announced in a letter circulated publicly shortly after the stock markets closed Monday that in mid-October, the Treasury would exhaust the “extraordinary measures” to keep the government from overextending its borrowing authority.

“At that point, the United States will have reached the limit of its borrowing authority, and Treasury would be left to fund the government with only the cash we have on hand on any given day. The cash balance at that time is currently forecasted to be about $50 billion,” Lew wrote.

The upcoming spending debates on Capitol Hill will almost converge, setting up a tough slog in September and October.

Copies of the letter went to House and Senate leaders in both parties, and it was copied to all other lawmakers, including the chairmen and ranking members of the two tax-writing committees.

“Extending borrowing authority does not increase government spending; it simply allows the Treasury to pay for expenditures Congress has previously approved. Protecting the full faith and credit of the United States is the responsibility of Congress because only Congress can extend the nation’s borrowing authority,” Lew added. “Failure to meet that responsibility would cause irreparable harm to the American economy.”

In that statement, Lew once again swore off any alternative measure for handling the debt ceiling that relies only on executive branch action, such as making a declaration that the debt ceiling is unconstitutional under the 14th Amendment.

Initial response from Capitol Hill was predictable.

“With just nine legislative days currently scheduled in September, Republicans must return to Congress prepared to move beyond the kind of brinksmanship that undermined our economic recovery two years ago. It is time for Republicans to do the right thing — not the far right thing — and put the American economy first,” House Ways and Means ranking member Sander M. Levin, D-Mich., said in a statement. “Congress must pay its bills based on the legislative bills that it has passed, living up to our obligations and paying our bills just like the American family does.”

“The debt limit remains a reminder that, under President Obama, Washington has failed to deal seriously with America’s debt and deficit,” Michael Steel, a spokesman for Speaker John A. Boehner, R-Ohio, said in an emailed statement.

Of course, the timing is such that even before the debt ceiling endgame, lawmakers must address funding for the federal government from Oct. 1 onward, when the next fiscal year begins. The House and Senate have yet to agree on any of the regular appropriation bills for the next fiscal year, with a disagreement between the chambers on the topline spending level, as well as a push by some GOP lawmakers to use the stopgap spending bill as a means to choke off funding for the 2010 health care overhaul.

The two debates seem likely to collide anyway, since Boehner told his conference on a call last week that he plans to push for a stopgap continuing resolution to keep the government funded at lower spending levels than Obama would like.

Of course, if lawmakers were able to reach a longer-term agreement in October, that could save members of Congress and their staffs from spending another holiday season in the Capitol, as has become the normal practice in recent years. Both chambers were in session on New Year’s Day of 2013.

Emma Dumain contributed to this report.

Correction: 8:16 p.m.

An earlier version of this article attributed a sentence to Treasury Secretary Jacob J. Lew that was not in his letter. The following was not in his letter: The upcoming spending debates on Capitol Hill will almost converge, setting up a tough slog in September and October.